Question #288192

The function f(x, y) =cos √x^3 +y^3 is a homogenous function. Say true or false.

1
Expert's answer
2022-01-18T06:54:48-0500
f(x,y)=cosx3+y3f(x, y)=\cos \sqrt{x^3+y^3}

f(kx,ky)=cos(kx)3+(ky)3f(kx, ky)=\cos \sqrt{(kx)^3+(ky)^3}

=cos(k3/2x3+y3)=\cos (k^{3/2}\sqrt{x^3+y^3})

Therefore the statement that the function f(x,y)=cosx3+y3f(x, y)=\cos \sqrt{x^3+y^3} is a homogenous function is False.


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